Why im not getting thickness with shrinkwrap modifier
The shrinkwrap modifier will flatten your mesh (as explained to you on your previous question) since it will move all vertices onto the target mesh.

As an alternative you can try using a lattice to deform the mesh and have the lattice use the swhinkwrap. As the lattice is deformed your mesh will undertake a similar deformation. 

Create a lattice with only one subdivision on the vertical axis. This is achieved via the Lattice properties in the properties panel (only visible when the lattice is selected - see the right-hand side of the image below). The Lattice properties define the number of U, V, W dimensions of the lattice. The dimensions default to 2, 2, 2 - effectively forming a cube. By increasing the dimensions in two directions (to give us some subdivisions) and setting the other dimension to 1 will form a plane. When the plane is deformed this can be used to affect your mesh - but since the lattice plane has no 'height' it also will not affect the 'height' of your mesh. Position the lattice along the baseline of the mesh you want to deform.



Add a lattice deform modifier to the design that you want to bend, and select the lattice object as the one to deform the mesh.



Now simply add a Shrinkwrap modifier to the lattice with the Target set to the surface you want to deform to. The lattice should now be deformed to the surface and your mesh will be deformed similarly. Adjust the Shrinkwrap distance and settings to fine-tune.